“To the extent principal reduction and other modification tools help us turn mortgages headed for possible foreclosure into long-term performing loans, it will be positive for homeowners, mortgage investors and communities,” Ron Sturzenegger, a legacy asset servicing executive, said in the statement.

The bank said it planned to contact more than 200,000 homeowners who could be candidates for the offers, sending letters to a majority of them by the third quarter of this year.

To be eligible for the principal reductions, however, homeowners will have to meet certain criteria, including: having a loan owned or serviced by Bank of America; owing more on the mortgage than their property is worth; and being at least 60 days behind on payments as of the end of January.

In the statement, the bank said it had started making such offers in March to a narrower group of homeowners — those who were already in the process of seeking mortgage modification. The bank estimated that the earlier wave of trial reduction offers to about 5,000 people could amount to more than $700 million in forgiven principal. But homeowners have to make at least three timely payments for the reductions to become permanent.